An innovative tactic to transportation problem in Fermatean fuzzy setting

In operations research, a transportation problem (TP) is a sort of optimization problem in which the goal is to determine the best cost-effective way to convey items from many different places of origin and destination. The basic goal of the transportation challenge is to reduce the overall expense of transportation when moving a product from a source to a destination. It is extremely challenging to characterize the transportation problem's data, like cost, demand, and supply, because of the unpredictable economic and environmental elements. In this paper, the fermatean fuzzy transportation problem (FFTP) is utilized to calculate the lowest cost of transporting products from origin to destination. It is believed that the most recent tools for effectively managing ambiguity and fuzziness are fermatean fuzzy sets. In this work, a new ranking function that converts Fermatean uncertain numbers into crisp form is developed. An initial basic feasible solution (IBFS) for three different kinds of transportation problems in fermatean settings is subsequently provided using a novel method known as the inverse coefficient of a range. Furthermore, we used the modified distribution (MODI) method to obtain the ideal outcome. To illustrate the suggested methodology, we tackled a series of numerical problems, and outcomes are offered together with a comparison of results to the findings of previous research. The significance of the study and the direction of future research are then emphasised.